The reference "as per family tradition" is really intriguing!
I wonder how many other brides in the family have worn the fringe as a wedding tiara? (I have to admit, I have not even tried to research that aspect)
The only one I know who wore a fringe tiara for her wedding is Caroline Dewar. At least that comment seems to solve the query of which fringe she wore.
(The current Duchess wore the the much grander tiara given to Princess Louise, Duchess of Fife by her husband -- that is the one which was accepted by the UK government in lieu of inheritance tax in recent years.)
I hope that some photos are released so that we can all see a modern image of the tiara being worn.